Extractions are a way to separate a desired substance when it is mixed with others.
The mixture is brought into contact with a solvent in which the substance of interest is soluble, but the other substances present are insoluble.

Extractions use two immiscible phases to separate the substance from one phase into the other.

Typical lab extractions are of organic compounds out of an aqueous phase and into an organic phase.
The distribution of a solute between two phases is an equilibrium condition described by partition theory.

Tea-making is a very basic non-laboratory extraction. You boil tea leaves in water to extract the tannins, theobromine, polyphenols, and caffeine out of the leaves and into the water.

Illustration of an extraction in a separatory funnel

Analytical Extractions

Elemental analysis generally requires fairly simple (not necessarily easy) sample preparation.
Solids are usually dissolved or digested in causticsolution and liquids are sometimes extracted to separate the analyte from interferences.

Organic analysis is often much more complicated.
Real-world samples can be very complicated matrices that require careful extraction procedures to obtain the analyte(s) in a form that can be analyzed.